Analytical and Numerical Analysis of Linear and Nonlinear Properties of an rf-SQUID Based Metasurface
| Autor: | Bernhard Maier, Carsten Rockstuhl, Marlis Hochbruck, Marvin M. Müller |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Electromagnetic field
Physics Field (physics) Numerical analysis Mathematical analysis FOS: Physical sciences Applied Physics (physics.app-ph) 02 engineering and technology Physics - Applied Physics 021001 nanoscience & nanotechnology 01 natural sciences Finite element method Nonlinear system 0103 physical sciences Reflection (physics) Equivalent circuit Boundary value problem 010306 general physics 0210 nano-technology |
| Popis: | We derive a model to describe the interaction of an rf-SQUID (radio frequency superconducting quantum interference device) based metasurface with free space electromagnetic waves. The electromagnetic fields are described on the base of Maxwell's equations. For the rf-SQUID metasurface we rely on an equivalent circuit model. After a detailed derivation, we show that the problem that is described by a system of coupled differential equations is wellposed and, therefore, has a unique solution. In the small amplitude limit, we provide analytical expressions for reflection, transmission, and absorption depending on the frequency. To investigate the nonlinear regime, we numerically solve the system of coupled differential equations using a finite element scheme with transparent boundary conditions and the Crank-Nicolson method. We also provide a rigorous error analysis that shows convergence of the scheme at the expected rates. The simulation results for the adiabatic increase of either the field's amplitude or its frequency show that the metasurface's response in the nonlinear interaction regime exhibits bistable behavior both in transmission and reflection. published in Physical Review B, Phys. Rev. B 99, 075401 |
| Databáze: | OpenAIRE |
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